Teenager Forrest and 25-year-old Martin, who was born in Brighton, are named in Craig Levein's pool for games against Wales and Republic of Ireland in Dublin later this month.
Leeds striker Ross McCormack and Blackpool goalkeeper Matt Gilks have been recalled, but in-form Wolves striker Steven Fletcher's international exile continues.
Stepping up: James Forrest (left) is in the Scotland squad to face Wales and Republic of Ireland
Levein was unable to call up the injured Alan Hutton, Craig Gordon and Graham Dorrans, while fitness reasons have forced Mark Wilson out.
Darren Fletcher is unavailable given Manchester United's participation in the Champions League final.
St Johnstone midfielder Murray Davidson and Watford's Don Cowie have dropped out of the squad following the defeat by Brazil in March, while Kilmarnock captain Craig Bryson and in-form Motherwell wide player Jamie Murphy have missed out.
In form: But Wolves striker Steven Fletcher (right) is not in Craig Levein's Carling Nations Cup squad
Peterborough striker Craig Mackail-Smith is in the squad after making his debut against Brazil, although his presence will depend on the outcome of the League One play-off semi-finals.
Levein has received constant updates about the form of right-back Martin from his club manager, former Scotland midfielder Paul Lambert.
'Russell has had a fantastic season at Norwich City, and congratulations to Paul and his backroom staff and players for getting promoted to the English Premier,' Levein said.
Scotland squad to face Wales and Republic of Ireland Goalkeepers: Gilks (Blackpool), McGregor (Rangers), Turner (Everton)
Defenders: Bardsley(Sunderland), Berra (Wolves), G Caldwell (Wigan), Crainey (Blackpool), Hanley (Blackburn), R Martin (Norwich), Whittaker (Rangers), Wilson (Liverpool)
Midfielders: Adam (Blackpool), Bannan (Aston Villa), Brown (Celtic), Forrest (Celtic), McArthur (Wigan), Morrison (West Brom), Robson (Middlesbrough), Commons (Celtic)
Forwards: Maguire (Aberdeen), Mackail-Smith (Peterborough), Naismith (Rangers), McCormack (Leeds), Miller (Bursaspor)
'Russell is one we have had our eye on for a while. He's in the squad but there are still elements of the paperwork to be finalised.
'If we can't get it done in time, so be it, but I'm confident. His father is Scottish so it shouldn't be too difficult.
'Norwich have been in the States celebrating and he has flown back early to get the paperwork done.'
Forrest, 19, has become a first-team regular with Celtic under Neil Lennon and joins fellow teenagers Danny Wilson and Grant Hanley in the squad.
Levein said: 'In keeping with adding young talented players to the groups in recent games, we have added James for this particular match because I feel he'll be an international footballer of some repute in years ahead.
'The idea is to get them used to travelling and being involved in international football so when they become regulars it's second nature to them.
'I believe it's much easier for a player to feel at home in international football if they feel involved. But I'm sure he's the type of player to bring a smile to people's faces.'
Levein described himself as a 'big admirer' of McCormack, who has recently returned to form with Leeds, and scored in a World Cup qualifier against Iceland in one of his five previous caps.
Out: Alan Hutton (left) is injured while Darren Fletcher has the Champions League final to look forward to
Wolves striker Fletcher has not been included since sending a text to a member of the Scottish Football Association staff to request not to be considered for the opening Carling Nations Cup game, a 3-0 win over Northern Ireland in February.
Levein said: 'The situation with Steven is exactly the same as before - if Steven indicates to me that he wants to be involved in the Scotland national team, then I'll consider him.'
When asked if the door was not closed for the former Hibernian striker, Levein said: 'He just needs to open it. I have absolutely no problem with Steven, as I've said in previous times, but really I'm here to talk about people who are selected.'
Scotland face Wales on May 25 before the tournament concludes with a game against the hosts, who beat Wales in February.
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Explore more:People: Mark Wilson, Steven Fletcher, Craig Gordon, Darren Fletcher, Craig Mackail-Smith, Alan Hutton, Craig Levein, Paul Lambert, Danny Wilson Places: Leeds, Liverpool, Brighton, Aberdeen, Norwich, Dublin, Scotland, Republic of Ireland, Wales, Brazil, Northern Ireland, Ireland Organisations: Scottish Football Association